Select independent or not independent for each description of events. p(a)=0.3, p(b)=0.5, p(a|b)=0.15 p(a)=0.2, p(b)=0.4, p(a|b)=0.2 p(a)=0.6, p(b)=0.2, p(a|b)=0.3

When two events X and Y are independent,

Then, P(X ∩ Y) = P(X) × P(Y)

We know that,

Thus, by substituting the value of P(X ∩ Y),

Which is the required condition for independent events.

In first option,

P(A)=0.3, P(B)=0.5, P(A|B)=0.15

⇒ A and B are not independent events

In second option,

P(A)=0.2, P(B)=0.4, P(A|B)=0.2

⇒ A and B are independent events.

In third option,

P(A)=0.6, P(B)=0.2, P(A|B)=0.3

⇒ A and B are not independent events

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9